Nonlinear nonconvex second order multivalued systems with maximal monotone terms

Abstract

We consider a multivalued system in RN driven by the vector p􀀀Laplacian, with maximal monotone terms and multivalued perturbations. The boundary condition is nonlinear and general and incorporate as special cases the Dirichlet, Neumann and periodic problems. We first prove the existence of extremal trajectories. Then, for the semilinear systems (that is, p = 2) and for particular boundary conditions, we prove a strong relaxation theorem, showing that the extremal trajectories are dense in the solution set of the convexified system.